Method and apparatus for determining the dip of aerial lines



Dec. 7 1926.

S. SANDBERG METHOD AND APPARATUS FOR DETERMINING THE DIP OF AERIAL LINES Filed May 1925 Appheation filed'May 13, 192-5 Serial No. 31,433, and in Norway December 8, 1923.

UNITED STATES PATENT OFFICE.

SVERBE SANTDBERG, 3F DRAMMEN, IQ'GRWAY, ASSIGNOR TO AKTIESELSKAPET NORSK ALUMINIUM COMPANY. OF OSLO, NORWAY.

IYIETEOD AND APIEARATUS FOR- DETERMINING THE DIP OF AERIAL LINES.

In the construction of aerial lines, prcierratio between the stress 8 and the variation ably electric lines it is desirable to have the of form 5: i. e.;

stretches of the linebetween the 5 suspension (masts) as tight as Ii possible, 1. e., with a minimum sag or dip,

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but on the other hand a certain maximum and instead of the Stress, the p g stress of the line mi'ast not be exceeded tension H and the Cross section My invention relates to a method and ap- H: a paratus for quickly determining the correct H dip of the line to be allowed between any two points of suspension.

My method is based on the fact that a line nus glves when freely suspended between two points 5 E i suspension, terms a catenary which beg: cause the cable 1s composed of unit lengths a a of equal weight is approximately a parabolio curve determined by the formula: or 02 26} Q22 s H=v ad (III) the derivation of which is found in Lue- If insert, instead of t Unit Weight; 9 in gers Lexikon der gesammten Technik vol.- q q the Cross Sectlon a and denslty IV, page 712 in which f is the dip, g the I Obtalna weight 01" a length unit of the line (cable), Z =ad the length of: the span between the points adl of suspension, and H the tension of the line. H W

If a part of a line thus suspended is given H= dl2 a quick tap at a point near either of the z points of suspension, there will thereby be (IV) started a transverse wave travelling towards the other point of suspension, which when Y combmlns aqua-Hons In and I reflected from this point will return to the Obtaln, y q g the Value f f,

pointof suspension from which it started. lz The time this transverse wave takes to E travel both ways (i. e., the double span width r QZ) is designated by 25 seconds. f l 90 According to the law found by Newton in W; the 38M E Finally I insert in this equation the time as the derivation of which is found in Luet Q) gers Lexikon der gesammten Technik vol. IV, page 71.2 in which 41 is the velocity of 2 the wave, and is dependent upon the coefli- 2 eient of elasticity E of the material and its 1 Z 1 I may here consider the density as uniand Obtam form, the waves being practically wholly This is of importance in so far T as in a transverse wave only the elasticity of f= form is involved, and not the elasticity of This equation gives the relation between introduce into equation (II) the the dip and the space of time used by the transverse wave to travel back and tortl.

The traetionhas by experiments been found to be con stant tor the various materials as copper aluminium and the like Instead of starting from the formula of Newton 1: may also start from the formula given for the velocity ofwaves by the English scientist Professor Tait, vizi the derivation of which ublished in his Dynamics, London 1895 in which E is the tensional stress or strain in the line, and 8 the mass of a length unit of the line.

When this formula is combined with the Formula (I) in a similar 7 ianner to the foregoing, I obtain the following equation for the dip of the line:

Ely 325 wherein 5 is a constant depending; on the form-elastic properties of the material used for the line, and g is the acceleration due to av y- Thus also in thisc a'se I a formula for the dip of the linebetween the two points of suspension expressed as a product ot a constant (dilierent for each particular material) and the square of the time used by the transverse wave.

This gives a means for making a table, giving for seconds and fractions of seconds observed, the corresponding dips, so that it is only necessary to observe the time used for the vibration to travel back and torth, to read oil direct the most desirable nip of the span in question. As the waves pass back and forth several times, I may, it desired, obtain a greater accuracy by repeating the time observations and taking the average thereot.

In accordance with my invention I use for observing the dip, an apparatus in the form r of a stop watch of known construction, which is provided with a dial having a division or scale, giving directly the dip tor the line material in question, corresponding to the time observed by the aid of the stop mechanism. 7

On the accompanying drawing, is shown, by way ot'example, such stop watch as used for this invention.

In the drawing; the outer scale 1, is the usual scale of minutes and fractions thereof. The inner scale 2, however, is arranged in conformity with the present invention, so that the position of the hand 3 directly gives the dip corresponding to the observed time,

according to the formula obtained above i. e.,

as a product of the square or" the time ob served, and a constant which depends upon the material used for the aerial line in question. Y

It will be understood that this apparatus may be used to dete mine the dip in mounting the line as well as to control lines already built.

I claim y p 1. A method of determining the dip of an aerial. line freely suspended between tvo points, comprising, starting a transverse wave in the line at one suspension point, and utilizing the time required by such wave to travel back and forth between the points of suspension, by the aid ot a scale, to determine the dip in the line as a function or the time of travelotthe wave. I p 2. method of deternining the dip of an aerial inens-31y suspended between two points, comprising, starting a transverse wave inthe line and utilizing the time required by ch wave to travel back and forth between the points of suspension, by aid 01" a scale, to determine the dip in the line as aproduct of the square ot the time or travel oi? thewave and constant depending onthe material of the line, V

In testimony whereof I have signed my name to this specification.

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